The Equivalence of Linearly Constrained Optimum Array Weight Vectors Under Different Optimisation Criteria

摘要

The performance of arrays of receivers can be improved by optimisation of the weighting vectors used to form the output beams. Three optimisation criteria are considered: minimisation of total output power, least mean square fit to a signal vector, and maximisation of signal-to-noise ratio. For practical purposes it is often necessary to apply some form of constraint to the weighting vectors. The optimum narrowband array weight vector is derived for each of the three criteria when an arbitrary set of linear constraints are imposed on the weight vector. The equality of the derived weight vectors in most cases of practical interest is proved. Finally, some examples are considered which show how a number of recently proposed weighting vectors can be derived as special cases of the constrained solutions.